On the robust estimation of power spectra, coherences, and transfer functions.

Robust estimation of power spectra, coherences, and transfer functions are investigated in the context of geophysical data processing. The methods described are generally frequency- domain extensions of proven techniques from the statistical literature and are applicable in cases where section-averaging methods would be used and where the data are contaminated by occasional bad values or "outliers." The paper begins with a review of robustness in statistics and robust estimation theory, with the emphasis on the maximum likelihood or M-estimators. These are then combined with section averaging spectral techniques to obtain robust power spectra, coherences, and transfer functions in an automatic, data- adaptive fashion. The importance of monitoring the effects on the statistics of the problem using quantile-quantile diagnostic plotting is also discussed. The results are illustrated using a variety of examples from electromagnetic geophysics. In particular, smooth, low-bias magnetotelluric response functions can be obtained using single station data that are often comparable in quality to remote reference results.